Hybrid method for randoms variance reduction

ABSTRACT

A method for reducing randoms variance in a Positron Emission Tomograph (PET) or Positron Emission Tomograph combined with another Medical Imaging device is disclosed. An average of an element of the randoms event (delayeds) sinogram may be estimated by dividing fan sums in delayeds sinogram by singles rates taken from headers of the delayeds sinogram.

TECHNICAL FIELD

The technical field of the present disclosure relates to noise reductionin tomography. More particularly, a system and method of the presentapplication allows a reduction of data variance due to randomscorrection in positron emission tomography (PET).

BACKGROUND

Random coincidences are a significant source of noise in, for example,PET. The raw data collected by a PET scanner may be a list ofcoincidence events representing near-simultaneous detection ofannihilation photons by a pair of detectors. Each coincidence eventrepresents a line in space connecting two detectors along which thepositron emission occurred. This line may be referred to as the line ofresponse (LOR).

Coincidence events can be sorted into groups of LORs, called sinograms,that represent projection views through the radionuclide distributionwithin the object being scanned. The sinograms may be sorted by theangle of each view around the axis of the scanner, as well as its tiltwith respect to this axis, the latter in the case of 3D acquisitions. Anormal PET data set has millions of counts for the whole acquisition,which may include a large component of undesirable scatter and randomevents. Considerable pre-processing of the data may be required, forexample, correction for random coincidences, estimation and subtractionof scattered photons, detector dead-time correction (after the detectionof a photon, the detector must “cool down” again) anddetector-sensitivity correction (for both inherent detector sensitivityand changes in sensitivity due to angle of incidence).

Consequently, there is considerable interest in developing methods andalgorithms that reduce the data variance due to, for example, randomcoincidence correction. To arrive at the true events in a PET scanner, asubtraction of the random coincidences, measured using a delayed, oroffset, coincidence window, from measured prompt coincidence events maybe done. However, since random coincidences are statisticallyuncorrelated with the prompt coincidences, this subtraction will cause arandom noise variance to be added to the corrected measured events. Theamount of noise added during this correction will be proportional to thenoise in the random coincidence estimate used. Thus this subtraction maymake methods reducing noise in the estimated random coincidencesattractive.

In view of the discussion above, there may be a need to provide a methodand a system allowing for reduction of randoms variance. Further, thesesystems and methods should preferably be easy to implement and/or fastto compute.

It is always sought to improve the image quality in tomography.Consequently, a system and method reducing randoms variance may improvethe final image quality in tomography.

Additionally, it may be desirable to provide a system and method thatallows for a more accurate and precise reduction of randoms variance. Amore accurate and precise reduction of randoms variance may be desirablefrom an economical and/or technical perspective.

SUMMARY

According to one embodiment a method may reduce randoms variance in aPositron Emission Tomograph (PET) or Positron Emission Tomographcombined with another Medical Imaging device. An averaged estimate of anelement, R_(ij), of the randoms event (delayeds) sinogram correspondingto detectors_(i) and _(j) in a detector ring of the PET or PET/MedicalImaging device may be expressed as

${\hat{R}}_{ij} = \frac{R_{i}R_{j}}{2{\tau\left( {\sum\limits_{i^{\prime} \in I_{i}}s_{i^{\prime}}} \right)}\left( {\sum\limits_{j^{\prime} \in J_{i}}s_{j^{\prime}}} \right)}$wherein R_(i) and R_(j) are fan sums for detectors_(i) and _(j); 2_(T)is the coincidence time window; the randoms relate to single event ratess_(i) and s_(j) in the detectors by R_(ij)=2_(TS) _(i) _(S) _(j) ; I_(j)is a set of detectors corresponding to the fan of detector_(j); andJ_(i) is a set of detectors corresponding to the fan of detector_(i).The embodiment may comprise the steps of estimating the numerator fromfan sums in the delayeds sinogram of the PET or PET/Medical Imagingdevice; and estimating the denominator from singles rates taken from theheader of the sinogram, or otherwise recorded.

According to further embodiments, estimating the denominator fromsingles rates taken from the header of the sinogram may be done byaveraging and/or interpolating the single rates over several detectors.The several detectors may be arranged as multiplexed groups known asbuckets, and/or rings.

According to a further embodiment, the averaged estimate of R_(ij) maybe used to correct for effects of randoms events in the PET orPET/Medical Imaging device.

According to one embodiment, a system for reducing randoms variance in aPositron Emission Tomograph (PET) or Positron Emission Tomographcombined with another Medical Imaging device, may include detectorsarranged in a detector ring in the PET or PET/Medical Imaging device;means for generating sinograms; and processing means. The processingmeans may be operable to express an averaged estimate of an element,R_(ij), of the randoms event (delayeds) sinogram corresponding to thedetectors_(i) and _(j) in the detector ring of the PET or PET/MedicalImaging device as

${\hat{R}}_{ij} = \frac{R_{i}R_{j}}{2{\tau\left( {\sum\limits_{i^{\prime} \in I_{j}}s_{i^{\prime}}} \right)}\left( {\sum\limits_{j^{\prime} \in J_{i}}s_{j^{\prime}}} \right)}$wherein R_(i) and R_(j) are fan sums for detectors_(i) and _(j); 2_(T)is the coincidence time window; the randoms relate to single rates s_(i)and s_(j) in the detectors by R_(ij)=2_(TS) _(i) _(S) _(j) ; I_(j) is aset of detectors corresponding to the fan of detector_(j); and J_(i) isa set of detectors corresponding to the fan of detector_(i). Theprocessing means may be further operable to estimate the numerator fromfan sums in the delayeds sinogram of the PET or PET/Medical Imagingdevice; and estimate the denominator from singles rates taken from theheader of the sinogram, or otherwise recorded.

According to further embodiments, the processing means may be furtheroperable to estimate the denominator from singles rates taken from theheader of the sinogram by averaging and/or interpolating the singlerates over several detectors. The several detectors may be arranged asbuckets and/or rings.

According to a further embodiment, the processing means may be furtheroperable to use the averaged estimate of R_(ij) to correct for theeffects of randoms events in the PET or PET/Medical Imaging device.

According to one embodiment, a method may reduce randoms variance in aPositron Emission Tomograph (PET) or Positron Emission Tomographcombined with another Medical Imaging device. An average of an elementof the randoms event (delayeds) sinogram may be estimated by dividingfan sums in delayeds sinogram by singles rates taken from the header ofthe sinogram, or otherwise recorded.

According to further embodiments, the singles rates taken from theheader of the sinogram may be averaged and/or interpolated single ratesover several detectors. The several detectors may be arranged as bucketsand/or rings.

According to a further embodiment, the averaged estimate of the elementmay be used to correct for effects of randoms events in the PET orPET/Medical Imaging device.

At least one of the embodiments may provide a system and method allowingfor reduction of randoms variance that is easy to implement and/or fastto compute. Furthermore, at least one of the embodiments may improve theimage quality in tomography.

Additionally, at least one of the embodiments may provide a system andmethod that allows for a more accurate and precise reduction of randomsvariance from an economical and/or technical perspective.

The herein described systems and methods relate to reduction of randomsvariance for PET. However, the herein described systems and methods mayalso apply to positron emission tomography combined with another MedicalImaging device, and/or other forms of tomography involving reduction ofrandoms variance.

The other Medical Imaging device in all embodiments may be, for example,an X-ray Computed Tomography scanner (PET/CT) or a Magnetic ResonanceImaging device (MRI).

Other technical advantages of the present disclosure will be readilyapparent to one skilled in the art from the following description andclaims. Various embodiments of the present application obtain only asubset of the advantages set forth. No one advantage is critical to theembodiments. Any claimed embodiment may be technically combined with anyother claimed embodiment(s).

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings, which are incorporated in and constitute apart of the specification, illustrate presently preferred embodiments ofthe invention, and together with the general description given above andthe detailed description of the preferred embodiments given below, serveto explain, by way of example, the principles of the invention.

FIG. 1 shows an embodiment of processing principles of a PET.

FIG. 2 shows and embodiment of detector fans for two detectors definingone LOR.

FIG. 3 shows an example of a measured randoms sinogram.

FIG. 4 shows an example of an estimated smoothed randoms sinogramgenerated by using an embodiment of the method.

FIG. 5 shows a line chart of counts/bins over sinogram bin numbercomparing profiles along central rows of the two sinograms in FIGS. 3and 4.

FIG. 6 is a flow chart of an exemplary embodiment of a method accordingto an embodiment.

DETAILED DESCRIPTION

FIG. 1 shows an embodiment of processing principles of a PET. A subject4, for example a patient, is positioned within a detector ring 3comprising photo-multiplier tubes (PMTs) 5. In front of the PMTs 5 areindividual crystals 8, also called detectors 8. A group of four PMTs mayhave an array of detectors 8 in front of them. For example, an array ofeight by eight or thirteen by thirteen detectors 8 (crystals) ispossible, but any other array may be selected. Each detector 8 may be anindividual crystal in front of respective PMT. During an annihilationprocess two photons 7 are emitted in diametrically opposing directionsas schematically illustrated in circle 6. These photons 7 are registeredby the PET as they arrive at detectors 8 in the detector ring 3. Afterthe registration, the data, resulting from the photons 7 arriving at thedetectors 8, may be forwarded to a processing unit 1 which decides iftwo registered events are selected as a so-called coincidence event. Allcoincidences are forwarded to the image processing unit 2 where thefinal image data may be produced via mathematical image reconstructionmethods. Before the data can be used by such a reconstruction method therandom variance may be reduced to exclude registered events that are nottrue events. A way of approaching this may be to subtract the randomcoincidences from the measured events. Hereby only the true eventsshould remain.

A PET scanner may register a detected coincidence event in either aprompt coincidence time window or a delayed coincidence time window. Thedelayed coincidences represent random (accidental coincidence) events,and the prompt coincidences represent true coincidences contaminated byrandom events and other events, such as for example scatter. The promptdata may be corrected for the effects of the random events bysubtracting the delayed coincidences. Such a subtraction compensates forthe random events in terms of the mean but increases the variance data.By estimating the mean of random events from the delayeds sinogram,these estimates may be incorporated to create an estimated smoothedrandoms sinogram useful for later image reconstruction.

One exemplary method is described with reference to FIG. 2. FIG. 2 showsan embodiment with detector fans for two detectors_(i) and _(j) definingone LOR. A number of detectors 8 form the detector ring 3. Looking atany one detector, for example _(i) in FIG. 2, data may be collected forthat detector in coincidence with many other detectors. This is what isreferred to as a fan. In other words, all the detectors for whichcoincidences are measured with the detector_(i) are called the fan fordetector_(i). The fan sum is then the sum of all data collected by thisset of detectors. In FIG. 2 the set of detectors 8 making up the fan fordetector_(i) is marked J_(i). The set of detectors 8 making up the fanfor detector_(j) is marked I_(j).

Let R_(ij) be an element of the randoms (delayeds) sinogramcorresponding to detectors_(i) and _(j). Assume that the randoms arerelated to the singles rates s_(i) and s_(j) in the detectors by:R_(ij)=2_(TS) _(i) _(S) _(j,)   (1)

where 2_(T) is the coincidence time window. Let I_(j) be the set ofdetectors for which there are LORs in the sinogram terminating at j,i.e., the fan of j. Similarly, let J_(i) be the fan of i. Then the fansums for i and j are:

$\begin{matrix}{{R_{i} = {{\sum\limits_{j^{\prime} \in J_{j}}R_{{ij}^{\prime}}} = {{\sum\limits_{j^{\prime} \in J_{i}}2_{{TS}_{i}S_{j^{\prime}}}} = {2_{{TS}_{i}}{\sum\limits_{j^{\prime} \in J_{i}}s_{i^{\prime}}}}}}}{R_{j} = {{\sum\limits_{i^{\prime} \in I_{j}}R_{i^{\prime}j}} = {{\sum\limits_{i^{\prime} \in I_{j}}2_{{TS}_{i^{\prime}}S_{i}}} = {2_{TSj}{\sum\limits_{i^{\prime} \in I_{j}}s_{i^{\prime}}}}}}}} & (2)\end{matrix}$

Solving these two relations for s_(i) and s_(j), and substituting intoequation (1), we have an expression for an averaged estimate of R_(ij)

$\begin{matrix}{{\hat{R}}_{ij} = \frac{R_{i}R_{j}}{2{\tau\left( {\sum\limits_{i^{\prime} \in I_{j}}s_{i^{\prime}}} \right)}\left( {\sum\limits_{j^{\prime} \in J_{i}}s_{j^{\prime}}} \right)}} & (3)\end{matrix}$

Unfortunately, without further constraints or approximations thedenominator in equation (3) cannot be expressed directly in terms ofsums over R_(ij). At least two approaches may be suggested to addressthis issue.

The first approach may be to assume that the sums in the denominator donot vary appreciably and replace them with a constant factor. Thissuggested “fan sum” approach is an approximate solution.

The second approach may be that an exact solution can be obtained byconstraining I_(j) and J_(i), such that they are fixed groups ofdetectors (i.e. do not vary with the _(i) or _(j) detectors withinthem), and further, such that each detector in one group is incoincidence with every detector in the other group (all possible LORsbetween the two groups are measured). In this “block” sum approach, theexpression for the randoms estimate becomes

$\begin{matrix}{{\hat{R}}_{A_{i}B_{j}} = \frac{R_{i}R_{j}}{\sum\limits_{i^{\prime}}{\sum\limits_{j^{\prime}}R_{i^{\prime}j^{\prime}}}}} & (4)\end{matrix}$

Although the suggested block sum method may be exact, it has thedrawback that it does not use all available data for the estimate.Consequently, the full potential of the randoms smoothing effect is notrealized.

A more sophisticated suggestion relating to this approach may be topermit the use of multiple pairs of blocks of detectors for theestimation, thereby improving the smoothing effect. Nevertheless, evensuch a technique still not takes full advantage of all the dataavailable for the estimation.

Returning to equation (3), the unconstrained sums in the denominator maybe the sums of the singles rates over the detectors in the two fans. APET scanner may have the capability of recording the singles rates inits detectors, at least at a coarse-grained level. The fan of any onedetector may be the half of all the detectors, typically the halfdirectly across from the detector of interest. The drawback of onlyhaving coarse-grained data is thus reduced, because, when consideringhalf of the available data, using fine resolution of the singles raterather than coarse-grained data may not be significant.

A sinogram may comprise two files, for example, a binary data file andan ASCII header file. The binary data file may record the coincidenceevents detected in each LOR, for both the prompt and delayed coincidencewindows. The header of a sinogram may comprise additional data, such asdate and time of scan, duration of scan, information on singles rates,etc. In some realizations, these two component files may be combinedinto a single file containing a header part and a binary data part. Inother realizations, the binary data are not organized into sinograms,but are recorded in time sequence of their measurement. This may bereferred to as a listmode file. Listmode format data may be histogrammedinto sinogram format as needed. Other organizations of the data are alsopossible

Since the fan is typically half a ring, the averaging of the singlesentailed may be a fairly accurate and robust estimation of thedenominator of equation (3). Furthermore, on certain tomographs data ofthe singles rate for estimating the denominator in equation (3) may beavailable at, for example, a bucket block-ring level (one rate averagedover each block ring in each bucket). For example, an array of four byfour blocks of PMTs may form one bucket and a certain amount of buckets,for example sixteen buckets, may form one detector ring unit. The numberof detectors in a block, the number of blocks in a bucket, and thenumber of buckets in a detector ring unit may differ from tomograph totomograph. For example an eight by eight (or thirteen by thirteen) arrayof detectors (crystals) may form one block of detectors. Four PMTs maybe behind each block. For example sixteen blocks may be called a bucket.In a tomograph with four rings of block detectors, the bucket 9 mayextend over four rings axially and over four blocks radially. An exampleof such a bucket 9 is shown in FIG. 1. Thus, a bucket block ring mayrefer to the average across four blocks that are in one bucket and inone of the four block rings. The single rates may be averaged overseveral detectors 8 and interpolations may be made when the fan spansover parts of buckets.

With reference to equation (3), the numerator may express the fan sumsfor detectors_(i) and _(j). These fan sums may be estimated from fansums in the delayed sinogram.

Consequently, in an embodiment, a method or a system for reducingrandoms variance may comprise that the numerator in equation (3) may beestimated from fan sums in the delayeds sinogram, while the denominatormay be estimated from the singles rates taken from the sinogram header.This hybrid method has the advantage that it uses all available data inboth the delayeds sinogram and single rates to estimate a given randomsrate.

Although theoretically equation (3) is an exact method, there may besome residual error due to the coarse-graining of the singles. However,the method or the system may be more accurate than the suggested fan sumapproach, and may be more precise than the suggested block sum approach.

The method is easy to implement and very fast to compute because themethod works with data already present and available. At least oneembodiment based on this method may improve the image quality in atomography, because more measured data is used for reducing the randomsvariance.

The system is easy to implement and very fast to compute because thesystem works with data already present and available. At least oneembodiment based on this system may improve the image quality in atomography, because more measured data is used for reducing the randomsvariance.

One embodiment may show an example of how a smoothed randoms sinogramusing an embodiment of the method or the system may be generated.Further such a smoothed randoms sinogram may be compared to a measuredrandoms sinogram. In the embodiment, single event rates may be read fromthe header of the sinogram data files that result from a PETacquisition. These singles values may be interpolated to estimate asingles rate s_(i) for each detector in the scanner. Maps, for examplein the form of tables or arrays of numbers, relating each sinogram binto the two corresponding detectors may be generated. Using these maps,for each detector the fan sum of delayed coincidences in the measuredsinogram is formed as:

$\begin{matrix}{R_{i} = {\sum\limits_{j^{\prime} \in J_{i}}R_{{ij}^{\prime}}}} & (5)\end{matrix}$

The corresponding sum over all singles rates in the fan may also becomputed as:

$\begin{matrix}{\sigma_{i} = {\sum\limits_{j^{\prime} \in J_{i}}s_{j^{\prime}}}} & (6)\end{matrix}$

For each detector, the ratio of these two quantities may be formed as:

$\begin{matrix}{\rho_{i} = {\frac{R_{i}}{\sigma_{i}} = \frac{\sum\limits_{j^{\prime} \in {Ji}}R_{{ij}^{\prime}}}{\sum\limits_{j^{\prime} \in {Ji}}S_{j^{\prime}}}}} & (7)\end{matrix}$

Then the value for each bin in the output smoothed randoms sinogram isestimated by taking the product of the two corresponding values ofρ_(i). The sinogram may be indexed by a radial bin index b and aprojection angle index a. Each sinogram bin then corresponds to twodetectors, i(a,b) and j(a,b). A preliminary estimated smoothed randomsrate for this bin is then estimated by{circumflex over (R)}′_(a,b)=ρ_(i(a,b))ρ_(j(a,b))  (8)

To account for the 2T factor, and any numerical imprecision, thisestimate may then be scaled by a single multiplicative factor chosen sothat the total of the estimated smoothed randoms is equal to the sum ofthe measured delayed coincidences in the sinogram. The final estimate ofthe smoothed randoms sinogram may then be

$\begin{matrix}{{{\hat{R}}_{a,b} = {\alpha\;{\hat{R}}_{a,b}^{\prime}}},{where}} & (9) \\{\alpha = \frac{\sum\limits_{i,j}R_{i,j}}{\sum\limits_{a,b}{\hat{R}}_{a,b}^{\prime}}} & (10)\end{matrix}$

In a more specific embodiment a scan from a NEMA NU 2-2001 count ratetest with a 70 cm long phantom, at high activity, was performed. Thesingles rate was 46.7 Mcps, and the randoms/net trues ratio was 2.4. Onesinogram from this data set was considered. This measured delayeds(random coincidence) sinogram is shown in FIG. 3. The correspondingestimated smoothed randoms sinogram R_(a,b) is shown in FIG. 4. Thecalculation of this smoothed sinogram took less than 1 second. As may betaken from the FIGS. 3 and 4, the estimated sinogram is less noisy thanthe measured sinogram. FIG. 5 shows a line chart of counts/bins oversinogram bin number comparing profiles along central rows of the twosinograms in FIGS. 3 and 4. As may be taken from the FIG. 5, thestructure of the randoms distribution is accurately reproduced. Therandoms per bin vary by a factor of 2.5 across the sinograms.

According to one embodiment, a method may comprise the steps as outlinein the flow chart in FIG. 6. The exemplary method for reducing randomsvariance is suitable for use in a Positron Emission Tomograph (PET) orPositron Emission Tomograph combined with another Medical Imaging devicesuch as an X-ray Computed Tomography scanner (PET/CT) or MRI device. Asa first step, outlined in box 601, an average of an element of therandoms event (delayeds) sinogram is estimated by dividing fan sums in adelayeds sinogram by singles rates taken from the header of thesinogram.

The singles rates may be taken from the header of the sinogram indifferent ways, depending on the internal configuration of the PET,PET/CT or PET/MRI. As outlined in box 602, the singles rates taken fromthe header of the sinogram may be averaged and/or interpolated singlerates over several detectors. These detectors may be arranged in acertain structure influencing the possibilities for how the singlesrates are registered in the headers of the sinograms. According to box603, the several detectors may be arranged as buckets and/or rings.

According to one embodiment a method may use the averaged estimate of asinogram element to correct for effects of randoms events in the PET,PET/CT or PET/MRI. This is outlined in box 604.

At least one embodiment provides for a system and a method that allowsfor a more accurate and precise reduction of randoms variance. Asmentioned above, the implementation of at least one embodiment allowsfor a fast computing for reducing random variance and consequently makesembodiments desirable from an economical and/or technical perspective.

The system and method discussed above reduces randoms variance. Theinvention, therefore, is well adapted to carry out the objects andattain the ends and advantages mentioned, as well as others inherenttherein. While the invention has been described and is defined byreference to particular preferred embodiments of the invention, suchreferences do not imply a limitation on the invention, and no suchlimitation is to be inferred. The invention is capable of considerablemodification, alteration, and equivalents in form and function, as willoccur to those ordinarily skilled in the pertinent arts. The describedpreferred embodiments of the invention are exemplary only, and are notexhaustive of the scope of the invention. Consequently, the invention isintended to be limited only by the spirit and scope of the appendedclaims, giving full cognizance to equivalents in all respects.

1. A method for reducing randoms variance in a Positron EmissionTomograph (PET) or Positron Emission Tomograph combined with anotherMedical Imaging device, wherein an averaged estimate of an element,R_(ij), of a randoms event (delayeds) sinogram corresponding todetectors_(i) and _(j) in a detector ring of the PET or PET/MedicalImaging device is expressed as${\hat{R}}_{ij} = \frac{R_{i}R_{j}}{2{\tau\left( {\sum\limits_{i^{\prime} \in I_{j}}s_{i^{\prime}}} \right)}\left( {\sum\limits_{j^{\prime} \in J_{i}}s_{j^{\prime}}} \right)}$wherein R_(i) and R_(j) are fan sums for detectors_(i) and _(j); 2_(T)is the coincidence time window; the randoms relate to single rates s_(i)and s_(j) in the detectors by R_(ij)=2_(TS) _(i) _(S) _(j) ; I_(j) is aset of detectors corresponding to the fan of detector_(j); and J_(i) isa set of detectors corresponding to the fan of detector_(i); the methodcomprising the steps of: estimating the numerator from fan sums in thedelayeds sinogram of the PET or PET/Medical Imaging device; estimatingthe denominator from recorded singles rates; using the resultingaveraged estimate of R_(ij) as a randoms event (delayeds) sinogram. 2.The method according to claim 1, wherein the Medical Imaging device isan X-ray Computed Tomography scanner or a Magnetic Resonance Imaging(MRI) device.
 3. The method according to claim 1, wherein the singlerates are recorded in the header of the sinogram.
 4. The methodaccording to claim 3, wherein estimating the denominator from singlesrates taken from the header of the sinogram comprises averaging orinterpolating the single rates over several detectors.
 5. The methodaccording to claim 4, wherein the several detectors are arranged asbuckets and/or rings.
 6. The method according to claim 3, whereinestimating the denominator from singles rates taken from the header ofthe sinogram comprises averaging and interpolating the single rates overseveral detectors.
 7. The method according to claim 6, wherein theseveral detectors are arranged as buckets and/or rings.
 8. The methodaccording to claim 1, the method further comprising the step of usingthe averaged estimate of R_(ij) to correct for effects of randoms eventsin the PET or PET/Medical Imaging device.
 9. A method for reducingrandoms variance in a Positron Emission Tomograph (PET) or PositronEmission Tomograph combined with another Medical Imaging device, whereinan average of an element of a randoms event (delayeds) sinogram isestimated by dividing fan sums in the delayeds sinogram by recordedsingles rates.
 10. The method according to claim 9, wherein the MedicalImaging device is an X-ray Computed Tomography scanner or a MagneticResonance Imaging (MRI) device.
 11. The method according to claim 9,wherein the single rates are taken from the header of the sinogram. 12.The method according to claim 11, wherein the singles rates taken fromthe header of the sinogram are averaged or interpolated single ratesover several detectors.
 13. The method according to claim 12, whereinthe several detectors are arranged as buckets and/or rings.
 14. Themethod according to claim 11, wherein the singles rates taken from theheader of the sinogram are averaged and interpolated single rates overseveral detectors.
 15. The method according to claim 14, wherein theseveral detectors are arranged as buckets and/or rings.
 16. The methodaccording to claim 9, the method further comprising the step of usingthe averaged estimate of the element to correct for effects of randomsevents in the PET or PET/Medical Imaging device.